Hot Water

I think about water a lot. I live in a place not much wetter than most deserts so I think about water a lot. I was thinking about the energy we use to heat water. I have to think that a hot shower is the only thing that gets most people out of bed and off to work. Coffee perhaps a second, and that takes hot water, too. It takes one BTU to raise a pound of water one degree on the Fahrenheit scale. That’s about a pint of water, and even at a mild two-gallons-per-minute a modest five-minute shower takes ten gallons which is 80 pints. If it comes out of the tap at 55 ºF and I want to shower at 105 ºF that’s an increase of 60 degrees. Eighty times sixty is 4800. That’s how many BTUs it takes for what for most of us would consider a “quick rinse.” My quick-and-dirty calculation actually undershoots* the value a bit, it’s closer to 5000 BTU, and that seems like an easy number to work with.

My dad was always simplifying things when it came to math. It seems he hated to calculate, all he wanted was “a rough figure” as he liked to put it. I remember assiduously figuring the exact number of yards of concrete for some project, a walk or a driveway or a patio or something, and excitedly announcing it. I was just a kid and I liked math. Anyway it was some fractional amount like 2.4, and my dad had already quickly estimated it to be “around two-and-a-half” which meant “we’ll have to get three” which I missed entirely in my zeal to be precise. Of course the concrete place only sold it in whole-yard units, which was the lesson. Dad knew how imprecise he could be in the problem, and always rounded off numbers to ones that were easy to work with. It’s a lovely skill, I picked it up quickly, and of all the math I learned it’s the one I use the most. And the one I found most difficult to teach. Trying to get kids to approach a math problem playfully, where there’s wiggle room to guess and estimate is so contrary to traditional practice as to be almost impossible. But that’s for another post.

My point today is this hot water luxury we first-worlders indulge in daily: it takes a lot of energy. I don’t want to get into the water itself, which is drinking-water pure, something hundreds of millions of our fellow humans have a hard time getting. That’s for another post. I’m thinking just of the natural gas or coal or nuclear power or solar energy or what-have-you that goes into heating the water. 5000 BTUs per shower, 300-plus million folks in the US of A or at least 100 million households, and I’m saying two showers per household per day. I think I’m underestimating here quite a bit, but that’s OK. Multiply 5000 times 2 times 100 million and you get ONE TRILLION BTUs.

That’s a lot of anything, one trillion. That’s 10^12 or ten-to-the-twelfth-power or ten times itself twelve times. So, can we get a sense of 5000 BTUs? That’s a five-minute hot shower. That’s as basic to our middle-class existence as breathing and eating. That shower takes 5000 BTUs and all of us showering requires at least a TRILLION of those things. Each day. So in a year (365 days) that’s about 365 trillion BTUs

Looking at the bigger picture, we here in the States used 97.4 QUADRILLION BTUs in 2016. A quadrillion BTUs is called a quad. Let’s divide: 365 trillion or 3.65 E14 by 97.4 quads or 9.74 E16 (I have to bust out the slide rule for this one) and I get 3.7 E−3 or 0.0037. The Jim O’Connor method would have made 365 into 400 and 97.4 into 100 and so the answer would be “4” of something. The decimals have to get moved, a quadrillion is a thousand times bigger than trillion, so you get 4÷1000 or 4/1000 or 0.004 which is close enough. So our showers need, conservatively, 0.004 quads of energy. That’s less than 1% of our total. A poor country like Chad uses about 0.005 quads of energy in a year. It has about 13 million people.

Any kind readers out there who’ll check my math? I’d be obliged; those skills fade with retirement!



*ten gallons of water is 83.45 pounds


6 thoughts on “Hot Water

  1. No real need for daily showers. Heck, we are just going to get dirty again anyway, right? I figure 3 days a week is plenty. So, multiply your numbers by 3/7 and that may result in a really substantial savings. Enough to water our yards, perhaps???


  2. The math seems correct. The US Energy Information Administration provides this breakdown of energy usage: Electric power = 39%; Transportation = 29%; Industrial – 22%; Residential = 6%; and Commercial = 4%. So of the 97.4 quads, 5.8 quads are used in residential. That includes cooking and heating and, electric power consumption by things like tvs, lights, computers and toasters. The 39% that the electric power sector consumes is for the generation of electricity. So 0.4 quads is 6.9, or 7% of home energy usage. Sound OK? Seems about right to me.


    • I appreciate the check! I love ‘back of the envelope’ calculations. I like to quantify things that are quantifiable–I mean, if one can work up a quick number to get a handle on the size of something, why not?


  3. Well the most likely error is an error of a factor of 10. So because neither 70% nor 0.7% pass the common sense test for household energy usage, you are likely correct.


    • That’s another part of the Jim O’Connor method: if the answer doesn’t make sense, move the decimal and call it good!

      Back in my math teaching days we called it “A Test of Reasonableness” but it sure turned out to be a hard thing to teach which of course seemed utterly unreasonable to me.


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